Related papers: Classifying Material Implications over Minimal Log…
When aggregating logically interconnected judgments from $n$ agents, the result might be inconsistent with the logical connection. This inconsistency is known as the doctrinal paradox, which plays a central role in the field of judgment…
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
A sceptical examination of the motivations for strong modal plural logics.
Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a…
Every definite logic program has as its meaning a least Herbrand model with respect to the program-independent ordering "set-inclusion". In the case of normal logic programs there do not exist least models in general. However, according to…
The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former…
This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of…
We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…
We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is…
Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $p\wedge\Diamond\neg p$ ('$p$, but it might be that not $p$') appears to be a…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
Two different paradoxes of the fuzzy logic programming system of [29] are presented. The first paradox is due to two distinct (contradictory) truth values for every ground atom of FLP, one is syntactical, the other is semantical. The second…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new…
In this article we determine the implicational fragments of most of the known subintuitionistic logics.
Counterfactual explanations are gaining prominence within technical, legal, and business circles as a way to explain the decisions of a machine learning model. These explanations share a trait with the long-established "principal reason"…